Details

Time bar (total: 5.7s)

sample37.0ms

Algorithm
intervals
Results
15.0ms250×body80valid
4.0ms13×body1280valid
3.0ms11×body640valid
2.0ms10×body320valid
1.0ms5×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
0236
1465
21285
33625
410245
522965
650015

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (- t x) (- a z))
12.9b
(fma (- y z) (/ (- t x) (- a z)) x)

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt *-un-lft-identity
25×times-frac
14×add-cube-cbrt
12×distribute-lft-out-- difference-of-squares
5×associate-/r* associate-/l*
4×add-exp-log add-cbrt-cube
2×pow1 expm1-log1p-u flip3-- associate-/r/ flip-- log1p-expm1-u associate-/l/ add-log-exp
1×cbrt-undiv frac-2neg div-sub div-exp clear-num fma-udef div-inv
Counts
2 → 64
Calls
2 calls:
12.0ms
(/ (- t x) (- a z))
0.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

series142.0ms

Counts
2 → 6
Calls
2 calls:
49.0ms
(/ (- t x) (- a z))
93.0ms
(fma (- y z) (/ (- t x) (- a z)) x)

simplify56.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 3 (50.0ms)

IterNodesCost
0268450
1733425
22490423
35001421

prune202.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 5.6b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- t x) (- a z))
2.2b
(+ (* (- y z) (/ (- t x) (- a z))) x)
5.4b
(* (- y z) (/ (- t x) (- a z)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
73×*-un-lft-identity
51×times-frac
31×associate-*r*
27×add-cube-cbrt
23×distribute-lft-out-- difference-of-squares
10×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-*l* associate-/r* flip-- associate-/l* add-log-exp
4×associate-/r/
3×expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-times div-exp associate-*l/ prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative fma-def frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip-+
Counts
3 → 126
Calls
3 calls:
12.0ms
(/ (- t x) (- a z))
12.0ms
(+ (* (- y z) (/ (- t x) (- a z))) x)
35.0ms
(* (- y z) (/ (- t x) (- a z)))

series333.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(/ (- t x) (- a z))
151.0ms
(+ (* (- y z) (/ (- t x) (- a z))) x)
128.0ms
(* (- y z) (/ (- t x) (- a z)))

simplify57.0ms

Algorithm
egg-herbie
Counts
135 → 135
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0489904
12048854
25001852

prune351.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 3.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
1.5b
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
7.1b
(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
75×add-sqr-sqrt
59×*-un-lft-identity
52×times-frac
46×associate-*r*
37×cbrt-prod
27×add-cube-cbrt
25×add-exp-log
18×cbrt-div add-cbrt-cube
17×associate-*l*
16×distribute-lft-out-- difference-of-squares
10×associate-/r/
9×flip3-- flip--
8×prod-exp cbrt-unprod
7×cbrt-undiv div-exp
6×pow1 add-log-exp unswap-sqr
5×frac-times
4×expm1-log1p-u log1p-expm1-u
3×associate-*r/ associate-*l/
2×pow1/3 div-inv
1×+-commutative fma-def flip3-+ pow-prod-down sum-log *-commutative flip-+
Counts
4 → 143
Calls
4 calls:
2.0ms
(cbrt (- a z))
3.0ms
(cbrt (- a z))
77.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
34.0ms
(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

series787.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(cbrt (- a z))
156.0ms
(cbrt (- a z))
303.0ms
(* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z))))
179.0ms
(+ (* (/ (- y z) (* (cbrt (- a z)) (cbrt (- a z)))) (/ (- t x) (cbrt (- a z)))) x)

simplify94.0ms

Algorithm
egg-herbie
Counts
155 → 155
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
07581907
133161731
250011632

prune514.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.3b

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
0.6b
(cbrt (- a z))
3.2b
(+ (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))) x)

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
15×cbrt-prod
13×add-sqr-sqrt *-un-lft-identity
7×add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×flip3-- pow1/3 flip-- distribute-lft-out-- difference-of-squares
1×+-commutative fma-def flip3-+ sum-log flip-+
Counts
4 → 65
Calls
4 calls:
2.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
2.0ms
(cbrt (- a z))
80.0ms
(+ (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))) x)

series628.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(cbrt (- a z))
152.0ms
(cbrt (- a z))
147.0ms
(cbrt (- a z))
176.0ms
(+ (* (/ (* (cbrt (- y z)) (cbrt (- y z))) (cbrt (- a z))) (* (/ (cbrt (- y z)) (cbrt (- a z))) (/ (- t x) (cbrt (- a z))))) x)

simplify121.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
0274766
1834709
24278680
35001651

prune508.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.3b

regimes276.0ms

Accuracy

24.5% (6.4b remaining)

Error of 10.2b against oracle of 3.7b and baseline of 12.3b

bsearch145.0ms

Steps
ItersRangePoint
10
2.259566323536502e-155
6.2675468718428e-145
2.7208315653629824e-146
10
-1.0079355577464942e-127
-1.318076215244674e-137
-9.101722715344051e-129

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03023
13023

end0.0ms

sample1.1s

Algorithm
intervals
Results
478.0ms7730×body80valid
120.0ms495×body640valid
80.0ms419×body320valid
73.0ms252×body1280valid
33.0ms285×body160valid
4.0ms10×body2560valid